Do ETF management custodians like vanguard have price sensitivity when they’re rebalancing?

Not sure if anybody here would know this, but this is something I’ve wondered about pricing/ buy timing for ETFS that rebalance: Imagine you have a 50/50 gold silver etf. Gold has gone up 70% since the last rebalancing period and silver has gone up 150%. Since the ETF is now overweight silver, they sell silver and buy gold to rebalance. What I’m wondering is if the powers at be who run this ETF are price sensitive: Ie; would they repetitively sell silver at the highest possible price to lock in profits, or are they unconcerned with that and really only trying to profit off of management fees. Seems like there is selling exclusively at 80 dollars an ounce right now for silver, and buying up to that point. Obviously that could be normal market dynamics, but I am trying to discern whether or not this is perhaps due to price selective selling by ETFs: apparently the necessary rebalancing that has to occur in the next few weeks or so is enough to drop the price by 13%.